Dislocations in covalent materials: the puzzling complexity of - PowerPoint PPT Presentation

Dislocations in covalent materials: the puzzling complexity of cores. Laurent Pizzagalli Institut P', CNRS, Poitiers University, France Laurent Pizzagalli GDR PULSE 2017

Part I Dislocations in III-nitrides Stoichiometry + structure = diversity Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

III-nitride compounds (GaN, AlN, InN) and dislocations Applications of III-nitride compounds concern for instance LED (AlN) and PV (InN) Threading dislocations N. Lobo Ploch, PhD thesis (2015) A. Mogilatenko et al., J. Cryst. Growth (2014) The presence of dislocations can degrade (or even suppress) opto- electronics properties → Calculations to evaluate/predict/understand the influence of dislocations Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Dislocations in GaN Ga-rich conditions N-rich conditions M. Matsubara et al., Appl. Phys. Lett. (2013) J. Northrup et al., Phys. Rev. B (2002) Different dislocation core positions and stoichiometries lead to multiple configurations Dislocation core structures for AlN and InN in different growth conditions? Influence of the most stable cores on electronic properties? Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Dislocation modeling: Full PBC system 2 dislocations with opposite Burgers vectors Non-orthogonal periodic conditions Initial conf. from elasticity theory DFT calculations Quantum Espresso code Plane-waves basis, cutoff 40 Ry PAW GGA-PBE 3 special k-points (disl. line) For electronic structure: HSE06 hybrid calculations 4 special k-points (disl. line) Dependence on supercell size: 128/288 atoms Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Investigated dislocation cores: A-type Al × N Dislocation centered on one hexagon Initial configurations from a full Al core to a full N core Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Investigated dislocation cores: B-type Al N × Dislocation centered between two hexagons Initial configurations from a full Al core to a full N core Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Energy considerations μ max (exp.) μ max (calc.) Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Energy considerations Non-stoichiometric configurations are favored for both Al-rich and N-rich conditions An open depleted core (minimal core distortions) is found in mid-range Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Electronic structure: Al-rich conditions HSE06 calc. Presence of metallic states associated to Al core atoms (Al-Al distance like in bulk Al), deep into the gap. Possible leakage currents along the dislocation line (like in GaN) Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Electronic structure: intermediate conditions HSE06 calc. Presence of shallow states on Al-atoms and of deep empty states on N- atoms: possible non negligible influence on electronic properties Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Electronic structure: N-rich conditions HSE06 calc. Deep states associated to triple bonds between core N atoms Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Energy considerations: InN Non-stoichiometric configurations are favored for In-rich and mixed conditions A stoichiometric configuration is obtained in N-rich conditions Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Comparison between III-nitrides III-rich conditions: metallic-like III-filled dislocation cores N-rich conditions (GaN/InN): open (AlN, GaN) or filled (InN) bond-centred core, according to strength of bonds N-rich conditions (AlN): N-filled core only for AlN (high formation enthalpy) Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Part I conclusions Structure and stability of dislocation cores in III-nitrides In III-rich conditions, a core filled with atoms III (Al, In, Ga) is found as the energetically most stable one. Metallic-like states are associated to this core, which could be a source of leakage currents In intermediate conditions, a bond-centered core, depleted (for AlN) or filled with In, is found. In N-rich conditions and AlN, two original N-filled cores are predicted to be more stable. These cores are characterized by the presence of N-N triple or double bonds. Associated electronic levels are located deep into the electronic gap. L. Pizzagalli et al., Phys. Rev. Materials 2 , 064607 (2018) Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Part II Dislocations in silicon The plot thickens Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

High-temperature plasticity of (ductile) silicon Si 1050°C Dissociated dislocations Partials with 30° and 90° orientations High activation energies for mobility (Q ≈ 2.2 eV) Peierls mechanism : thermally activated formation/migration of kinks 30° 90° sp 90° dp Dislocation core structure is known from calculations Duesbery, Jones, Heggie, Bulatov, Yip, Vanderbilt, Jacobsen, Sutton, Payne, Sankey, Öberg, Kaxiras, and many others → T wo quasi-degenerate core structures for 90° partial dislocations → Anti-phase defects (solitons) likely along dislocation line → High number of possible confjgurations / mechanisms for kinks → Few theory works on the interaction with impurities: Jones, Heggie, Ewels, Justo Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Plastic deformation at low temperature / high stress Rabier et al MSE (2004) Non-dissociated dislocations Screw (wavy), 60°, 30°, and 41° orientations Rabier et al PSS (2007) Izumi et al PML (2010) High stresses, about 1-1.5 GPa J. Rabier et al., in Dislocations in solids, vol 16 , ch. 93, p47 (2010) Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

State of the art, until recently… A C 2 2 possible screw dislocation cores C 2 is more stable but less mobile X X Nucleation/mobility → A is dominant G S3 S1 2 stable sessile 60° cores 1 transient mobile core L. Pizzagalli et al., Phys. Rev. Lett. 103 , 065505 (2009) Little importance for “bulk” applications Low temperature Great importance for nanostructures (nanowires, fjlms) high stress Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Plastic deformation of silicon nanostructures Wagner et al., Acta Mat. (2015) F. Hoffman et al., Adv. Func. Mat. (2009) Kizuka et al., PRB (2005) Nano-objects have been elastically deformed up to very large strains (>10%) A brittle-ductile transition is observed for small sizes Influence of large strains on dislocation cores Could a dislocation core leads to crack initiation? local disorder? Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Dislocation modeling: hybrid cluster-PBC system Initially locked in positions given by anisotropic elasticity theory Ease electronic structure calculations Allow for applying strain DFT calculations Quantum Espresso code Plane-waves basis, cutoff 20 Ry PAW LDA 2 special k-points DFTB calculations DFTB+ code pbc-0.3 Slater-Koster parameters 5 special k-points Potential calculations SWm (L. Pizzagalli et al, JPCM 2013) MEAM (J. Godet et al, EML 2016) Tersoff (J. Tersoff, PRB 1989) 336 atoms Only one dislocation in the supercell The dislocation-surface interaction must be negligible Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Bi-axial strain deformation approach ε y Strain the initial configuration ↓ conjugate gradient relaxation No Poisson relaxation along z (negligible influence) ε x We do not know the most stable structure All 5 core geometries have to be tried for each strain state Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

60° dislocation core S1 S2 S3 The 'traditional' core Weakly stable with DFT Stable with DFT Stable with potentials Sessile!!! Unstable with DFT S4 S5 Closed core Open core All 5 cores must be computed for each stress state Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Bi-axial strain deformation map for the 60° dislocation S1 S2 S3 S4 S5 Amorphization The most stable dislocation core depends on the strain state Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Bi-axial tension (7.5%,7.5%) Initiation of crack S3 is the most stable for moderate tension The transformation dislocation core → crack is possible for tensile strains occuring in experiments Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

Bi-axial compression S4 could be the most stable conf. (-5%,-5%) Local disorder The most stable dislocation core depends on the strain state The transformation core → disorder occurs for moderate compression Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018

X-compression / Y-tension or X-tension / Y-compression (-5%,5%) S1 can be stabilized (5%,-5%) S2 can be stabilized too The most stable dislocation core depends on the strain state L. Pizzagalli et al., Philos. Mag. 98 , 1151 (2018) Laurent Pizzagalli Physics of Defects in Solids, T rieste, July 9-13 2018